Subgroups — C₄×C₁₃×#365 #15699008

Order 3328.

330 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#365	C₂	1	2	yes	maximal
2	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#108	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1383	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#108	C₂²	1	2	yes	—
9	C₂×C₁₃×#106	C₂²	1	2	yes	—
10	C₄×C₁₃×M₁₆	—	2	1	no	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
13	C₁₃×#365	C₄	1	8	yes	direct product factor
14	C₁₃×#346	C₄	1	2	yes	complemented
15	C₄×C₁₃×C₁₆	C₄	1	2	yes	complemented
16	C₁₃×#341	—	2	1	no	—
17	C₁₃×#340	—	2	1	no	—
18	C₂×C₁₃×M₁₆	—	2	2	no	—
19	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
22	C₂×C₄²×C₁₃	—	4	1	no	—
23	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
24	C₁₃×M₃₂	—	2	2	no	—
25	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
26	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
28	C₁₃×#108	—	2	2	no	—
29	C₁₃×#108	C₂×C₄	1	4	yes	—
30	C₁₃×#106	—	2	2	no	—
31	C₁₃×#106	C₂×C₄	1	4	yes	—
32	C₁₃×#97	—	4	1	no	—
33	C₄×C₈×C₁₃	—	4	1	no	—
34	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
37	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
38	C₁₃×#95	—	4	1	no	—
39	C₄×#365	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₄×C₁₃	—	4	2	no	—
41	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₁₃×M₁₆	—	2	4	no	—
45	C₁₃×M₁₆	—	4	2	no	—
46	C₂×C₈×C₁₃	—	2	2	no	—
47	C₂×C₈×C₁₃	—	4	2	no	—
48	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
52	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₁₃	#41	1	2	yes	—
54	C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₁₃×C₄⋊C₄	—	4	2	no	—
56	C₄²×C₁₃	—	8	2	no	—
57	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
58	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
59	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
60	C₄²×C₁₃	SD₁₆	1	1	yes	characteristic
61	C₁₃×C₁₆	—	2	2	no	—
62	C₁₃×C₁₆	C₄²	1	4	yes	complemented
63	C₂×#365	C₂×C₁₃	1	2	yes	—
64	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic
65	C₄×#108	C₂×C₁₃	1	1	yes	characteristic
66	C₄×#106	C₂×C₁₃	1	1	yes	characteristic
67	#1383	C₂×C₁₃	1	2	yes	—
68	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	4	1	no	—
71	C₂×C₄×C₁₃	—	4	4	no	—
72	C₂×C₄×C₁₃	—	8	2	no	—
73	C₂×C₄×C₁₃	—	8	2	no	—
74	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
80	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#135	1	2	yes	—
82	C₈×C₁₃	—	2	1	no	—
83	C₈×C₁₃	—	2	1	no	—
84	C₈×C₁₃	—	4	4	no	—
85	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
86	C₈×C₁₃	#117	1	1	yes	characteristic
87	C₈×C₁₃	C₄×Q₈	1	2	yes	—
88	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
89	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
90	C₂×#108	C₂²×C₁₃	1	2	yes	—
91	C₂×#106	C₂²×C₁₃	1	2	yes	—
92	C₄×M₁₆	—	2	1	no	—
93	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
94	C₄×C₄⋊C₄	—	2	1	no	—
95	#365	C₄×C₁₃	1	8	yes	direct product factor
96	#346	C₄×C₁₃	1	2	yes	complemented
97	C₄×C₁₆	C₄×C₁₃	1	2	yes	complemented
98	#341	—	2	1	no	—
99	#340	—	2	1	no	—
100	C₂²×C₁₃	—	2	1	no	—
101	C₂²×C₁₃	—	2	1	no	—
102	C₂²×C₁₃	C₂×#106	1	1	yes	characteristic
103	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
104	C₄×C₁₃	—	2	1	no	—
105	C₄×C₁₃	—	2	1	no	—
106	C₄×C₁₃	—	2	1	no	—
107	C₄×C₁₃	—	8	4	no	—
108	C₄×C₁₃	#365	1	2	yes	direct product factor
109	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
110	C₄×C₁₃	#427	1	1	yes	characteristic
111	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
112	C₂×M₁₆	—	2	2	no	—
113	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
114	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
115	C₂×C₄⋊C₄	—	2	2	no	—
116	C₂×C₄²	—	4	1	no	—
117	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
118	M₃₂	—	2	2	no	—
119	M₃₂	C₂×C₄×C₁₃	1	4	yes	—
120	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
121	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
122	#108	—	2	2	no	—
123	#108	C₂×C₄×C₁₃	1	4	yes	—
124	#106	—	2	2	no	—
125	#106	C₂×C₄×C₁₃	1	4	yes	—
126	#97	—	4	1	no	—
127	C₄×C₈	—	4	1	no	—
128	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
129	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
130	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
131	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
132	#95	—	4	1	no	—
133	C₂×C₁₃	—	2	2	no	—
134	C₂×C₁₃	C₄×#106	1	1	yes	characteristic
135	C₂×C₁₃	C₂×#365	1	1	yes	characteristic
136	C₂×C₁₃	#2155	1	1	yes	characteristic
137	C₂²×C₄	—	4	2	no	—
138	C₂²×C₄	C₁₃×SD₁₆	1	1	yes	characteristic
139	C₂²×C₄	C₁₃×SD₁₆	1	1	yes	characteristic
140	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
141	M₁₆	—	2	4	no	—
142	M₁₆	—	4	2	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	4	2	no	—
145	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
148	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
149	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
150	C₂×C₈	C₁₃×#41	1	2	yes	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	4	2	no	—
153	C₄²	—	8	2	no	—
154	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
155	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
156	C₄²	C₁₃×SD₁₆	1	1	yes	characteristic
157	C₄²	C₁₃×SD₁₆	1	1	yes	characteristic
158	C₁₆	—	2	2	no	—
159	C₁₆	C₄²×C₁₃	1	4	yes	complemented
160	C₁₃	C₄×#365	1	1	yes	characteristic, direct product factor, Sylow
161	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	4	1	no	—
164	C₂×C₄	—	4	4	no	—
165	C₂×C₄	—	8	2	no	—
166	C₂×C₄	—	8	2	no	—
167	C₂×C₄	C₁₃×#106	1	1	yes	characteristic
168	C₂×C₄	C₁₃×#106	1	1	yes	characteristic
169	C₂×C₄	C₁₃×#106	1	1	yes	characteristic
170	C₂×C₄	C₁₃×#106	1	1	yes	characteristic
171	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
173	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
174	C₂×C₄	C₁₃×#135	1	2	yes	—
175	C₈	—	2	1	no	—
176	C₈	—	2	1	no	—
177	C₈	—	4	4	no	—
178	C₈	C₂×C₄²×C₁₃	1	1	yes	characteristic
179	C₈	C₁₃×#117	1	1	yes	characteristic
180	C₈	C₄×Q₈×C₁₃	1	2	yes	—
181	C₂²	—	2	1	no	—
182	C₂²	—	2	1	no	—
183	C₂²	C₂×C₁₃×#106	1	1	yes	characteristic
184	C₂²	C₄×C₁₃×SD₁₆	1	2	yes	—
185	C₄	—	2	1	no	—
186	C₄	—	2	1	no	—
187	C₄	—	2	1	no	—
188	C₄	—	8	4	no	—
189	C₄	C₁₃×#365	1	2	yes	direct product factor
190	C₄	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
191	C₄	C₁₃×#427	1	1	yes	characteristic
192	C₄	C₄×C₁₃×SD₁₆	1	2	yes	—
193	C₂	—	2	2	no	—
194	C₂	C₄×C₁₃×#106	1	1	yes	characteristic
195	C₂	C₂×C₁₃×#365	1	1	yes	characteristic
196	C₂	C₁₃×#2155	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#106
commutator	C₈	C₂×C₄²×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#106
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. C₁₃×#365	C₄	direct (N × H)
14. C₁₃×#346	C₄	semidirect
15. C₄×C₁₃×C₁₆	C₄	semidirect
39. C₄×#365	C₁₃	direct (N × H)
62. C₁₃×C₁₆	C₄²	semidirect
95. #365	C₄×C₁₃	direct (N × H)
96. #346	C₄×C₁₃	semidirect
97. C₄×C₁₆	C₄×C₁₃	semidirect
108. C₄×C₁₃	#365	direct (N × H)
159. C₁₆	C₄²×C₁₃	semidirect
160. C₁₃	C₄×#365	direct (N × H)
189. C₄	C₁₃×#365	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#365	2
C₄×C₁₃×M₃₂	2
C₄×C₁₃×#108	2
C₄×C₁₃×#106	2
C₁₃×#1383	2
C₄×#365	13

Subgroups — C4×C13×#365 #15699008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#365 #15699008